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III. ACASESTUDY:RESOURCEALLOCATIONIN quantumcomputeroperatorcanrequestthedeploymentofnew |
DISTRIBUTEDQUANTUMCOMPUTING quantum computers, or the utilization of on-demand quantum |
computingmayberequired.Shortly,quantumcomputingfrom |
A. Allocating Resources in Distributed Quantum Computing |
multipleorganizationscanbesharedinwhichoneorganization |
In the proposed distributed quantum computing framework, can borrow or buy quantum computing time from another |
a quantum computer operator serves quantum computation organization temporarily. Such a scenario is inspired by the |
tasks by distributing each of them to one or multiple quantum presentconventionalcloudcomputingparadigm.Forexample, |
computers that can work collaboratively to accomplish the Amazon Braket offers on-demand quantum cloud computing |
quantum computation. Quantum tasks may require the num- services [13]. For this option, the quantum computer operator |
ber of qubits, which each quantum computer provides. The installs and configures the on-demand quantum computers to |
works collaboratively with the deployed quantum computers. first part is the first-stage cost of using the reserved quantum |
Inaddition,thecostofusingthedeployedquantumcomputers computers and the second part is the expected second-stage |
islessthaninstallingthenewquantumcomputer.Utilizingthe cost that consists of the computing power unit and Bell pair |
deployedquantumcomputerwillcostthecomputingpowerof costs of the deployed quantum computers including the on- |
the quantum computer and the Bell pair of the two connected demand quantum computer deployment under the set of the |
quantum computers. However, using an on-demand quantum possible realized demand of quantum tasks, computing power |
computer is more expensive. The objective of the quantum of quantum computers, and fidelity of the entangled qubits. |
computer operator is to satisfy the quantum computing tasks The constraints of the stochastic programming model are |
while minimizing the total deployment cost. the selection of the utilized quantum computers, both the |
deployed and the on-demand quantum computers being able |
C. Uncertainty of Distributed Quantum Computing |
to complete the computational tasks, and the utilization of the |
Whiledeterminingthebestresourceallocationindistributed computingpowerunderthelinkcapacity,withconsideringthe |
quantum computing, uncertainties occur, which can be classi- uncertainty. |
fied into three types as follows: |
E. Experimental Results |
• First, the actual demands are unknown when the option |
of deploying the quantum computer is made. Different 1) Parameter Setting: We consider the system model of |
applicationssuchasminimization,dimensionalreduction, quantum computing where the quantum computer operator |
and machine learning problems may request various consists of 10 deployed quantum computers. We set the cost |
qubits [14]. For example, up to 30 qubits are used in values, which is measured in normalized monetary, for using |
machine learning problems [14]. the deployed quantum computer, qubits, and Bell pairs to be |
• Second, the precise availability of the quantum computer 5000, 1000, and 450, respectively. All quantum computers |
and its qubits is uncertain since they might be reserved have 257 qubit capacities and identical costs. The cost and |
for other purposes or because the quantum computer’s computing power of new quantum computer deployment are |
backend may not support all of them [15]. For example, 25000 and 127, respectively. Costs for both on-demand and |
only5of10quantumcomputersareavailabletocompute quantumcomputersaredeterminedbasedon[1],[13].Tosolve |
quantum tasks. theproposedstochasticmodel,weconsidertwoscenarios.The |
• Third, the fidelity of the entangled qubits is also not first scenario is that the demand of the quantum task is 10, |
known exactly due to the degradation of the entangled the available computing power of the quantum computers is |
qubits in distributed quantum computing [12]. For exam- 127qubits,andthefidelityoftheentangledqubitsinquantum |
ple, if the fidelity is 0.5, it means that 50% efficiency of networksis1(i.e.,thebestperformance).Thesecondscenario |
the entangled qubits can be achieved. is that there is no demand, no availability of qubits, and zero |
Therefore,anadaptiveresourceallocationapproachisrequired fidelity of the entangled qubits in quantum networks (i.e., the |
to efficiently provision quantum computers to tackle quantum worst performance). We assume the default probability values |
computational tasks with dynamic sizes under uncertainty with 0.8 and 0.2, respectively. |
of the computing power of quantum computers and fidelity 2) Impact of Probability of Scenarios: We vary the prob- |
fidelity of the entangled qubits. ability of the first scenario, which corresponds to having the |
demand, the availability of the quantum task, and the best |
D. The Proposed Approach |
performance for the entangled qubits. The cost breakdown is |
Inthedeterministicresourceallocationforcomputingquan- shown in Fig. 3b. We note that when the probability of the |
tum tasks in distributed quantum computing, the required scenario is equal to or less than 0.2, the new quantum com- |
demand of quantum tasks, the computational power of quan- puter should be deployed. The deployed quantum computer is |
tum computers, and the fidelity of the entangled qubits are utilized over the new quantum computer when the probability |
exactly known by the quantum computer operator. Therefore, of the scenario is higher as it has the demand of the quantum |
quantum computers can be certainly deployed and the on- task,computingpowerofquantumcomputers,andthefidelity. |
demandquantumcomputerdeploymentisnotnecessary.How- 3) Cost Comparison: We compare the proposed stochastic |
ever, due to the aforementioned challenges and the uncertain model with both the Expected Value Formulation (EVF) |
environmentsindistributedquantumcomputing,thedetermin- model and the random model. The EVF model solves the |
istic resource allocation approach is not applicable and the deterministic model using the average values of the uncertain |
on-demand deployment will be the solution. Therefore, we parameters. The cost of the new quantum computer deploy- |
proposetheadaptivedistributedquantumcomputingapproach ment is varied. In the random model, the deployed quantum |
based on the two-stage stochastic programming model. The computer in the first stage is randomly selected. Figure 3a |
first stage defines the number of deploying the reserved quan- depicts the comparison of total costs of the three models. |
tum computers, while the second stage defines the number of We observe that the proposed model achieves the lowest total |
installing the on-demand deployment of quantum computers. cost. The minimum total cost cannot be guaranteed by using |
The stochastic programming model can be formulated as the the average values of the uncertain parameters used in the |
minimization of the total cost including two parts, where the EVF. In addition, the EVF and random models are unable |
tum mechanics. According to the increased amount of IoT- |
1e4 |
connected devices, the scalability of utilizing one quantum |
Total Cost |
8 Dep. QC Cost computer needs to be extended to enhance the overall deploy- |
Comp. Cost ment using the properties of distributed quantum computers. |
Comm. Cost 3) Future UAV Trajectory Planning: Optimizing UAVs |
tsoC 6 Dep. new QC Cost trajectory is challenging when knowledge of ground users, |
e.g., locations and channel state information, are unknown. |
latoT |
4 Quantum-inspired reinforcement learning (QiRL) approach |
adopts superposition and amplitude amplification in quantum |
mechanics to select probabilistic action and strategy solved |
2 |
by conventional reinforcement learning on classical comput- |
ers [7]. The actual quantum computers, including distributed |
0 |
quantum computing, are required to improve convergence |
0.0 0.2 0.4 0.6 0.8 1.0 speed and learning effectiveness. |
Probability of demand scenarios ( 1) These applications may all be categorized as large-scale |
(a) Cost breakdown under different probabilities problems in future networks, which are still challenging be- |
cause of the numerous computational resources and processes |
1e5 |
required. A fresh solution to these problems could be further |
Proposed model addressed by the distributed quantum computing paradigm. |
1.6 |
EVF model Furthermore, classical and quantum computers will still coex- |
1.4 Random model ist to execute computational tasks. Hybrid computing, which |
tsoC combines quantum and classical computing, is required to |
1.2 significantly reduce energy consumption and costs. |
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